Math 120 Final Exam Review

Math 120 Final Exam ReviewSolve:1. 2x 2 – x – 28 = 02. (x + 4) 2 = 813. 4x 2 + 4x = 74. x 4 - 5x 2 + 6 = 05. x 4 + 4x 2 = 126 86. + = 3x x + 57.4 3− = 1x + 1 x + 28. 3x + 2 = 79.2x − 10 = x − 10x10. x − x − 5 = 111. x + 5 = x − 5Perform the indicated operation and write the answer in standard form:12. (5 + i) + (6 – 2i)13. (8 – i) – (4 + 3i)14. (1 + i)(2 – 3i)15. (6 – 2i)(1 + 2i)For 16-19, determine if the following equations represent a function:16.17.yy3= x +2 23+ x = 418. x = y − 219. y = x − 1

20. Find P(3) givenp( x)= ⎨⎩2⎧ x + x + if x 0.

For 31-34, match each graph with its corresponding function.31. y = 3x+ 232.33.34.x+ y = 252 2y = +y22x33= x −4a. bc d35. Find the slope of the line 3x + 2y = 5.36. Find the slope of the line 4y – 2x = 9For 37-40, determine if the function is even, odd, or neither:37.38.3h( x) = x + 5xf ( x) = 4x23239. f ( x)= x − 2x− 340.g( x)= x − x2 4

For 41-43, write the quadratic equations in standard form:41.42.43.f x x x2( ) = − + 2 + 1f x x x2( ) = 2 − 3 + 5f x x x2( ) = − 4 + 644. Divide:3 2(4x − 7x − 11x + 5) ÷ (4x+ 5)3 245. Divide: ( 6x − 16x + 17x − 6) ÷ (3x− 2)46. Use the Rational Zeros Theorem to list all the possible rational zeros of47. Use the Rational Zeros Theorem to list all the possible rational zeros off x x x x3 2( ) = 3 − 4 + 7 − 10f x x x x3 2( ) = 6 + 10 + + 848. If the leading coefficient of a 5 th degree polynomial with real coefficients is negative, describe the far-leftand far-right behavior of the graph.49. If the leading coefficient of a 4 th degree polynomial with real coefficients is positive, describe the far-leftand far-right behavior of the graph.50. If the leading coefficient of a 3 rd degree polynomial with real coefficients is positive, describe the far-leftand far-right behavior of the graph.51. Factor to find all the zeros of3 2f ( x) = 4x − 25x + 6x52. Z varies jointly with x and y. If z = 24 when x = 4 and y = 8, find z when x = 7 and y = 3.53. Y is varies inversely as x. If y = 3 when x = 25, find y when x = 20.54. X varies directly as y. If x = 9 when y = 2, find x when y = 7.55. Find the vertical asymptotes ofR( x)=23x− 12x+ 326x− 5x−1156. Solve:26x− 7x− 24 ≤ 057. Find the equation of a quadratic function that opens up and has x-intercepts at (4,0) and (8,0).58. Write in exponent form: log3x = 6 .59. Write as a single log: log5(3x+ 1) − 2log5(2x+ 11)60. Write as a single log: 2[2ln x − ln( x + 1) − ln( x − 1)]

61. Solve: log2x + log2( x − 4) = 262. Solve:2 15 x+ = 4863. Simplify:2 2log2(4 • 3 )664. Simplify: ln e2965. Simplify: log1030066. Solve: log2x + log2( x + 2) = log2( x + 6)67. Solve: 8 x = 468. Solve: log5x = − 369. Solve:⎛ 1 ⎞⎜ ⎟⎝ 2 ⎠X= 32−170. Find f ( x)if f ( x) = 2x+ 5−171. Find f ( x)if3x−1f ( x)=22x72. Write log bzyin terms of separate logs of x, y, and z. Assume x > 0, y > 0, z > 0 .73. Write as a single log: ln x − 4[ln( x + 2) + ln( x − 2)]74. Write as separate logs:ln62x +175. Write as a single log: ln x − 3ln( x + 1) .76. The number N of bacteria in a culture is modeled by N = 250ekt where t is the time in hours. If N = 280when t = 10, estimate the time required for the population to double in size.77. The half-life of radioactive radiumradium will remain after 100 years?226( Ra)is 1620 years. What percent of a present amount of radioactive

78. A deposit of $5000 is made in a trust fund that pays 7.5% interest, compounded continuously. It isspecified that the balance will be given to the college from which the donor graduated after the money hasearned interest for 50 years. How much will the college receive?79. Given+ − 2 + 6 + 9 = 0, find the center and radius of the circle.2 2x y x y80. From the graph, find the center and radius of the circle.x− 2 y = 0281. Solve:{3x− y = 082. Solve⎧⎨⎩x+ y =2 2xy2523 − 16 = 0{x − 2 y + 5 z = 283. The system4 x − z = 0had the following row echelon form solution⎡1 0 −.25 M 0 ⎤matrix: ⎢0 1 −2.625 −1⎥ . Determine the solution for the system, and state the type of solution.⎣M ⎦

⎧2x − 2y − 6z= −4⎪84. The system ⎨ − 3x + 2y + 6z= 1⎪ ⎩x − y − 5z= − 3has the following row echelon form solution matrix:⎡ 2 1⎤⎢1 − −2M −3 3⎥⎢⎥⎢0 1 3 M 5 ⎥ . Determine the solution for the system, and state the type of solution.⎢1 ⎥⎢0 0 1 M ⎥⎣2 ⎦85. The system⎧ 2x + y − z = 7⎪⎨x − 2y + 2z= − 9⎪ ⎩ 3x − y + z = 5has the following row echelon form solution matrix:⎡ 2 2 2 ⎤⎢1 − − M 13 3 3 ⎥⎢⎥⎢20 1 −1 M 6 ⎥ . Determine the solution for the system, and state the type of solution.⎢5 ⎥⎢⎥⎢0 0 0 M 1⎥⎢⎣⎥⎦

Answer Key71. x = 4, −22. x = − 13,5− 1±2 23. x =24. x = ± 2, ± 35. x = ± 2,± i 6106. x = 3, −37. x = 1, − 358. x = − 3, 39. x = − 1,1010. x = 911. no solution12. 11−i13. 4 − 4i14. 5 − i15. 10 + 10i16. yes17. no18. yes19. no20. P(3) = 1921. f (1) = − 122. g (4) = 3523. D :{ x | x ≥ −2}24. D :{ x | x ≠ −4,1}25. D : RD : x | x < 326. { }27.2y = − x + 7328. y = 2x29. d( −∞, −2) ∪ ( −1,1) ∪ 2, ∞30. ( )31. d32. b33. a34. c35.36.3m = −21m =237. odd38. even39. neither40. even241. f ( x) = −( x − 1) + 23 2 3142. f ( x) = 2( x − ) +4 8243. f ( x) = ( x − 2) + 2244. x − 3x+ 1245. 2x− 4x+ 31 2 5 1046. ± 1, ± , ± 2, ± , ± 5, ± , ± 10, ±3 3 3 31 1 1 2 4± 1, ± , ± , ± , ± 2, ± , ± 4, ± ,2 3 6 3 347.8± 8, ±348. far-left: up, far-right: down49. far-left: up, far-right: up50. far-left: down, far-right: up151. x = 0, ,646352. z = 15.75 or41553. y =4154. x = 31 255. x = − 156.57.x =116⎡ 3 8⎤⎢− ,⎣ 2 3⎥⎦2f ( x) = a( x − 12x + 32) where a > 0658. 3 = x59. log 3x+ 15 (2 11) 2x +60.2⎛ x ⎞ln ⎜⎟⎝ ( x + 1)( x − 1) ⎠61. 2 + 2 262. x ≈ 0.70363. 4 + 2log2364. ln 6 − 265. log103−266. x = 2267. x =32

168. x =12569. x = − 5−1 1 570. f ( x)= x −2 271. 1 ( )2 1−f x = x +3 3172. 2logb x + logb y − logbz273. ln x[( 2)( 2)] 4x + x −1 274. ln 6 − ln( x + 1)275. ln x( 1) 3x +76. t ≈ 61.16 hours77. 95.8%78. $212,605.4179. center: (1,-3); radius: 180. center: (-4,2); radius: 481. (0,0) and (12,6)82. (4,3) and (-4,3)83. (.25a, -1 + 2.625a, a), solution is consistent,dependent⎛ 1 1 ⎞84. ⎜3,3 , ⎟ , solution is consistent, independent⎝ 2 2 ⎠85. no solution, inconsistent